有不会的数学题？问问鸽子吧！

　　By now, the intelligence of birds is well known. Alex the African gray parrot had great verbal skills. Scrub jays, which hide caches of seeds and other food, have remarkable memories. And New Caledonian crows make and use tools in ways that would put the average home plumber to shame。

　　众所周知，鸟类极为聪明。一只名叫阿历克斯的非洲灰鹦鹉有不同寻常的口语能力；灌丛鸦能秘密隐藏种子和其他食物，有很强的记忆力；新喀里多尼亚鸦制作和使用工具的方式能让普通的家庭管道工自愧弗如。

　　Pigeons, it turns out, are no slouches either. It was known that they could count. But all sorts of animals, including bees, can count。

　　事实证明，鸽子的智力也不赖。它们会数数，这是尽人皆知的事实。但很多种动物，包括蜜峰，也会数数。

　　Pigeons have now shown that they can learn abstract rules about numbers, an ability that until now had been demonstrated only in primates。

　　近来人们研究发现，鸽子能学习抽象的数字规则，而这项能力目前为止仅在灵长目动物身上得以证实。

　　In the 1990s scientists trained rhesus monkeys to look at groups of items on a screen and to rank them from the lowest number of items to the highest。

　　在20世纪90年代，科学家们训练恒河猴，让它们看屏幕上的几组物品，并按物品数量从少到多的顺序进行排列。

　　They learned to rank groups of one, two and three items in various sizes and shapes. When tested, they were able to do the task even when unfamiliar numbers of things were introduced。

　　它们学会了按数量多少对几组物品进行排列， 每组都包含了一个、两个或三个不同形状和大小的物品 。在测试时，即使物品的数量它们不熟悉，也能完成任务。

　　In other words, having learned that two was more than one and three more than two, they could also figure out that five was more than two, or eight more than six。

　　也就是说，学会了两个比一个多，三个比两个多后，它们能够推理出五个比两个多，或八个比六个多。

　　Damian Scarf, a postdoctoral fellow at the University of Otago, in New Zealand, tried the same experiment with pigeons, and he and two colleagues report in the current issue of the journal Science that the pigeons did just as well as the monkeys。

　　达米安·斯卡夫是新西兰奥塔戈大学的博士后研究员，他对鸽子做了同样的实验。他和两个同事在本期的《科学》期刊上称鸽子在这方面的表现和猴子一样好。

　　Elizabeth Brannon, a professor of psychology and neuroscience at Duke University, and one of the scientists who did the original experiments with monkeys, was impressed by the new results. “Their performance looks just like the monkeys’,” she said。

　　杜克大学心理学和神经科学教授伊利莎白·布兰农，是最初给猴子做这种实验的科学家之一，对结果感到非常惊讶。“它们的表现竟和猴子一样。” 她说。

　　Score one for the birds. The pigeons had learned an abstract rule: peck images on a screen in order, lower numbers to higher。

　　给鸟类记上一分吧。鸽子已学会了一条抽象规则：按照数量从少到多的顺序轻啄屏幕上的图像。

　　It may have taken a year of training, with different shapes, sizes and colors of items, always in groups of one, two or three, but all that work paid off when it was time for higher math。

　　训练时每组图像都包含一个、两个或三个形状、大小、颜色各异的物品。这样的训练可能需要一年，但是等它们学习复杂点儿的数学时，就会发现这些付出是值得的。

　　Given groups of six and nine, they could pick, or peck, the images in the right order. This is one more bit of evidence of how smart birds really are, and it is intriguing because the pigeons’ performance was so similar to the monkeys’. “I was surprised,” Dr. Scarf said。

　　给它们几组包含六个和九个物品的图像，它们也能按正确顺序挑选或轻啄图像，证明了鸟类的确很聪明。这很耐人寻味，因为鸽子的表现和猴子的表现不相上下。“我很吃惊。”斯卡夫博士说。

　　He and his colleagues wrote that the common ability to learn rules about numbers is an example either of different groups — birds and primates, in this case — evolving these abilities separately, or of both pigeons and primates using an ability that was already present in their last common ancestor。

　　他和同事写道：鸽子和猴子都具有学习数字规则的能力，这表明不同的群组—这个案例中是鸟类和灵长类—要么是分别进化出这些功能，要么是遗传上一个共同祖先的能力。

　　That would really be something, because the common ancestor of pigeons and primates would have been alive around 300 million years ago, before dinosaurs and mammals. It may be that counting was already important, but Dr. Scarf said that if he had to guess, he would lean toward the idea that the numerical ability he tested evolved separately. “I can definitely see why both monkeys and pigeons could profit from this ability,” he said。

　　如果这项能力来自共同的祖先，那会意义非凡，因为鸽子和灵长类的共同祖先离现在已有三亿年了，那时恐龙和哺乳动物还没出现呢，很可能在当时数数已是很重要的能力了。但斯卡夫博士表示，如果让他进行猜测，他更倾向于这种能力是分别演化的这一观点。“我非常清楚为什么猴子和鸽子都能从这项能力中受益。”他说。

　　No testing has been done with numbers greater than nine, so whether a pigeon can count large numbers of bread crumbs or popcorn kernels is a question still open to investigation。

　　目前还没有大于9的数字测验，所以鸽子会不会数更多的面包屑或爆米花还有待进一步研究。